Evaluate: `int(cos^5x)/(sinx)\ dx`

Explanation

`int(cos^5x)/(sinx)\ dx`

`sinx = t=>cosx dx = dt`

`sn^2t+cos^2t=1`

`=int frac{(1-t^2)^2}{t}dt`

`=int frac{1+t^4-2t^2}{t}dt`

`=int 1/t dt+int t^3 dt- int 2t dt`

`=log abs(t)+frac{t^4}{4}-t^2`

`=log abs(sinx)+sin^4 (x/4)-sin^2x`